If I were in your position, I would make it a point to ask what the procedure is so you know what to expect in the unlikely event that the need should ever arise. Guest services should be able to answer this question. If guest services can't assist, I would keep asking even if you have to escalate to ship's safety officer. Your life is priceless.
I found this MSC page regard Special Needs, unfortunately it doesn't offer much applicable information to this thread. Also, here is a page from Safety4Sea which I interpret as each ship having its own idiosyncrasy and it comes down to communication between Passenger and Ship.
If memory serves, my training prior to working at NCL years ago had us transfer the passenger to a wheel chair and four crew members would carry the passenger down the stairs, one on each corner. I would imagine MSC does similar or has a stair rail system as mentioned in the Safety4Sea article above.
Agree, this beats the sweltering lineups on the promenade.
J